Study sheds more light on the chromatic decomposition of spaces
Chromatic homotopy theory – a subfield of stable homotopy theory – studies complex-oriented cohomology theories from the ‘chromatic’ point of view. This method decomposes a spectrum into monochromatic pieces. Each piece is a localised structure corresponding to one of the prime fields of higher algebra. The goal of the EU-funded ChromSpaces project is to study the chromatic decomposition of spaces rather than of a spectrum. It will establish structural results for the category of all monochromatic spaces ‘of a given colour’ and investigate how the original space can be built from its local pieces. The new techniques will be based on previous results associating monochromatic spaces to spectral Lie algebras, which generalise Quillen’s rational homotopy theory to all the other relevant chromatic localisations of homotopy theory.
Field of science
- /natural sciences/mathematics/pure mathematics/algebra
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